Prams and buggies are welcome on board trains. You may find it easier to get a buggy, rather than a pram, on and off trains – although there’s usually someone who will offer to help.
Don’t think you need to rush. Staff will be aware of you and won’t close doors until you are safely on. Please do ensure children are securely strapped in. Prams and buggies should be folded down once on board if at all possible.